Step by step
The question
Question: A lake has 6000 fish.
The number falls by 20% each year.
How many fish are there after 3 years?
1 Find the start and the factor
The start is 6000.
Each year it loses 20%.
So 80% is left.
80% is 0.8.
That is the factor.
start: a = 6000
100% − 20% = 80% = 0.8
factor: b = 0.8
2 Write the rule
x is the number of years.
Each year we multiply by 0.8 again.
So y = 6000 × 0.8ˣ.
y = 6000 × 0.8x
Careful!
0.2 is the part that is lost.
We multiply by the part that is left: 0.8.
Careful: not b = 0.2 ✗
3 Put in x = 3
After 3 years, x = 3.
y = 6000 × 0.83
0.8 to the power 3 is 0.512.
0.83 = 0.512
So we multiply 6000 by 0.512.
= 6000 × 0.512
So it is 3072.
= 3072
4 Check
Let's check year by year.
We start at 6000, and multiply by 0.8 each year.
After 3 years we get 3072 again.
It works!
after 3 years: 3072
Let's look back.
First: find the start and the factor.
Then: write the rule.
Then: put in x = 3.
Last: check.
Answer
= 3072